Related papers: Inference of Boundaries in Causal Sets
We consider the covering of a ball in certain normed spaces by its congruent subsets and show that if the finite number of sets is not greater than the dimensionality of the space, then the centre of the ball either belongs to the interior…
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of…
This paper develops a generalized framework for identifying causal impacts in a reduced-form manner under kinked settings when agents can manipulate their choices around the threshold. The causal estimation using a bunching framework was…
I present a way to visualize the concept of curved spacetime. The result is a curved surface with local coordinate systems (Minkowski Systems) living on it, giving the local directions of space and time. Relative to these systems, special…
Decomposition spaces are a class of function spaces constructed out of well-behaved coverings and partitions of unity of a set. The structure of the covering of the set determines the properties of the decomposition space. Besov spaces,…
The Minkowski content $L_0(G)$ of a body $G\subset{\mathbb{R}}^d$ represents the boundary length (for $d=2$) or the surface area (for $d=3$) of $G$. A method for estimating $L_0(G)$ is proposed. It relies on a nonparametric estimator based…
The paper is concerned with regularity properties of boundaries of causal pasts of points in a 3+1-dimensional Einstein-vacuum spacetime. In a Lorentzian manifold such boundaries play crucial role in propagation of linear and nonlinear…
Quantum integrable models that possess $N=2$ supersymmetry are investigated on the half-space. Conformal perturbation theory is used to identify some $N=2$ supersymmetric boundary integrable models, and the effective boundary…
Motivated by Wheeler's bottom up pregeometry, we introduce a pregeometric approach that does not assume Wheeler's probability amplitudes for establishing spacetime neighborhoods. Rather, a non-trivial metric is produced via the concept of a…
The Brunn-Minkowski theory relies heavily on the notion of mixed volumes. Despite its particular importance, even explicit representations for the mixed volumes of two convex bodies in Euclidean space are available only in special cases.…
We study 1-parameter families in the space $\mathscr{M}^G_1$ of $G$-invariant, unit volume metrics on a given compact, connected, almost-effective homogeneous space $M=G/H$. In particular, we focus on diverging sequences, i.e. which are not…
The estimation of surface integrals on the boundary of an unknown body is a challenge for nonparametric methods in statistics, with powerful applications to physics and image analysis, among other fields. Provided that one can determine…
We study 2d and 3d gravity theories on spacetimes with causal (timelike or null) codimension one boundaries while allowing for variations in the position of the boundary. We construct the corresponding solution phase space and specify…
Causal treatment effect estimation is a key problem that arises in a variety of real-world settings, from personalized medicine to governmental policy making. There has been a flurry of recent work in machine learning on estimating causal…
It is shown that continuous causal isomorphisms on two-dimensional Minkowski spacetime can be characterized by the invariance of wave equations.
Learning meaningful causal representations from observations has emerged as a crucial task for facilitating machine learning applications and driving scientific discoveries in fields such as climate science, biology, and physics. This…
Postulates which lead to Minkowski spacetime are amended in a subtle way, and used to construct a consistent flat spacetime geometry with intrinsic quantum character. Events in the new quantum geometry are described by labels of the form…
We propose a hyperbolic set-to-set distance measure for computing dissimilarity between sets in hyperbolic space. While point-to-point distances in hyperbolic space effectively capture hierarchical relationships between data points, many…
The causal structure of a strongly causal spacetime is particularly well endowed. Not only does it determine the conformal spacetime geometry when the spacetime dimension n >2, as shown by Malament and Hawking-King-McCarthy (MHKM), but also…
Gauge theories on manifolds with spatial boundaries are studied. It is shown that observables localized at the boundaries (edge observables) can occur in such models irrespective of the dimensionality of spacetime. The intimate connection…